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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.complex;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.io.Serializable;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.ArrayList;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.List;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.FieldElement;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math.MathRuntimeException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math.util.MathUtils;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * Representation of a Complex number - a number which has both a <a name="line.29"></a>
<FONT color="green">030</FONT>     * real and imaginary part.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * Implementations of arithmetic operations handle &lt;code&gt;NaN&lt;/code&gt; and<a name="line.32"></a>
<FONT color="green">033</FONT>     * infinite values according to the rules for {@link java.lang.Double}<a name="line.33"></a>
<FONT color="green">034</FONT>     * arithmetic, applying definitional formulas and returning &lt;code&gt;NaN&lt;/code&gt; or<a name="line.34"></a>
<FONT color="green">035</FONT>     * infinite values in real or imaginary parts as these arise in computation. <a name="line.35"></a>
<FONT color="green">036</FONT>     * See individual method javadocs for details.&lt;/p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * {@link #equals} identifies all values with &lt;code&gt;NaN&lt;/code&gt; in either real <a name="line.38"></a>
<FONT color="green">039</FONT>     * or imaginary part - e.g., &lt;pre&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;code&gt;1 + NaNi  == NaN + i == NaN + NaNi.&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * implements Serializable since 2.0<a name="line.42"></a>
<FONT color="green">043</FONT>     * <a name="line.43"></a>
<FONT color="green">044</FONT>     * @version $Revision: 791237 $ $Date: 2009-07-05 08:53:13 -0400 (Sun, 05 Jul 2009) $<a name="line.44"></a>
<FONT color="green">045</FONT>     */<a name="line.45"></a>
<FONT color="green">046</FONT>    public class Complex implements FieldElement&lt;Complex&gt;, Serializable  {<a name="line.46"></a>
<FONT color="green">047</FONT>        <a name="line.47"></a>
<FONT color="green">048</FONT>        /** Serializable version identifier */<a name="line.48"></a>
<FONT color="green">049</FONT>        private static final long serialVersionUID = -6195664516687396620L;<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>        /** The square root of -1. A number representing "0.0 + 1.0i" */    <a name="line.51"></a>
<FONT color="green">052</FONT>        public static final Complex I = new Complex(0.0, 1.0);<a name="line.52"></a>
<FONT color="green">053</FONT>        <a name="line.53"></a>
<FONT color="green">054</FONT>        /** A complex number representing "NaN + NaNi" */<a name="line.54"></a>
<FONT color="green">055</FONT>        public static final Complex NaN = new Complex(Double.NaN, Double.NaN);<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>        /** A complex number representing "+INF + INFi" */<a name="line.57"></a>
<FONT color="green">058</FONT>        public static final Complex INF = new Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);<a name="line.58"></a>
<FONT color="green">059</FONT>    <a name="line.59"></a>
<FONT color="green">060</FONT>        /** A complex number representing "1.0 + 0.0i" */    <a name="line.60"></a>
<FONT color="green">061</FONT>        public static final Complex ONE = new Complex(1.0, 0.0);<a name="line.61"></a>
<FONT color="green">062</FONT>        <a name="line.62"></a>
<FONT color="green">063</FONT>        /** A complex number representing "0.0 + 0.0i" */    <a name="line.63"></a>
<FONT color="green">064</FONT>        public static final Complex ZERO = new Complex(0.0, 0.0);<a name="line.64"></a>
<FONT color="green">065</FONT>        <a name="line.65"></a>
<FONT color="green">066</FONT>        /** <a name="line.66"></a>
<FONT color="green">067</FONT>         * The imaginary part <a name="line.67"></a>
<FONT color="green">068</FONT>         */<a name="line.68"></a>
<FONT color="green">069</FONT>        private final double imaginary;<a name="line.69"></a>
<FONT color="green">070</FONT>        <a name="line.70"></a>
<FONT color="green">071</FONT>        /** <a name="line.71"></a>
<FONT color="green">072</FONT>         * The real part <a name="line.72"></a>
<FONT color="green">073</FONT>         */<a name="line.73"></a>
<FONT color="green">074</FONT>        private final double real;<a name="line.74"></a>
<FONT color="green">075</FONT>        <a name="line.75"></a>
<FONT color="green">076</FONT>        /**<a name="line.76"></a>
<FONT color="green">077</FONT>         * Record whether this complex number is equal to NaN<a name="line.77"></a>
<FONT color="green">078</FONT>         */<a name="line.78"></a>
<FONT color="green">079</FONT>        private final transient boolean isNaN;<a name="line.79"></a>
<FONT color="green">080</FONT>        <a name="line.80"></a>
<FONT color="green">081</FONT>        /**<a name="line.81"></a>
<FONT color="green">082</FONT>         * Record whether this complex number is infinite<a name="line.82"></a>
<FONT color="green">083</FONT>         */<a name="line.83"></a>
<FONT color="green">084</FONT>        private final transient boolean isInfinite;<a name="line.84"></a>
<FONT color="green">085</FONT>        <a name="line.85"></a>
<FONT color="green">086</FONT>        /**<a name="line.86"></a>
<FONT color="green">087</FONT>         * Create a complex number given the real and imaginary parts.<a name="line.87"></a>
<FONT color="green">088</FONT>         *<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param real the real part<a name="line.89"></a>
<FONT color="green">090</FONT>         * @param imaginary the imaginary part<a name="line.90"></a>
<FONT color="green">091</FONT>         */<a name="line.91"></a>
<FONT color="green">092</FONT>        public Complex(double real, double imaginary) {<a name="line.92"></a>
<FONT color="green">093</FONT>            super();<a name="line.93"></a>
<FONT color="green">094</FONT>            this.real = real;<a name="line.94"></a>
<FONT color="green">095</FONT>            this.imaginary = imaginary;<a name="line.95"></a>
<FONT color="green">096</FONT>            <a name="line.96"></a>
<FONT color="green">097</FONT>            isNaN = Double.isNaN(real) || Double.isNaN(imaginary);<a name="line.97"></a>
<FONT color="green">098</FONT>            isInfinite = !isNaN &amp;&amp;<a name="line.98"></a>
<FONT color="green">099</FONT>            (Double.isInfinite(real) || Double.isInfinite(imaginary));<a name="line.99"></a>
<FONT color="green">100</FONT>        }<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        /**<a name="line.102"></a>
<FONT color="green">103</FONT>         * Return the absolute value of this complex number.<a name="line.103"></a>
<FONT color="green">104</FONT>         * &lt;p&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         * Returns &lt;code&gt;NaN&lt;/code&gt; if either real or imaginary part is<a name="line.105"></a>
<FONT color="green">106</FONT>         * &lt;code&gt;NaN&lt;/code&gt; and &lt;code&gt;Double.POSITIVE_INFINITY&lt;/code&gt; if<a name="line.106"></a>
<FONT color="green">107</FONT>         * neither part is &lt;code&gt;NaN&lt;/code&gt;, but at least one part takes an infinite<a name="line.107"></a>
<FONT color="green">108</FONT>         * value.&lt;/p&gt;<a name="line.108"></a>
<FONT color="green">109</FONT>         *<a name="line.109"></a>
<FONT color="green">110</FONT>         * @return the absolute value<a name="line.110"></a>
<FONT color="green">111</FONT>         */<a name="line.111"></a>
<FONT color="green">112</FONT>        public double abs() {<a name="line.112"></a>
<FONT color="green">113</FONT>            if (isNaN()) {<a name="line.113"></a>
<FONT color="green">114</FONT>                return Double.NaN;<a name="line.114"></a>
<FONT color="green">115</FONT>            }<a name="line.115"></a>
<FONT color="green">116</FONT>            <a name="line.116"></a>
<FONT color="green">117</FONT>            if (isInfinite()) {<a name="line.117"></a>
<FONT color="green">118</FONT>                return Double.POSITIVE_INFINITY;<a name="line.118"></a>
<FONT color="green">119</FONT>            }<a name="line.119"></a>
<FONT color="green">120</FONT>            <a name="line.120"></a>
<FONT color="green">121</FONT>            if (Math.abs(real) &lt; Math.abs(imaginary)) {<a name="line.121"></a>
<FONT color="green">122</FONT>                if (imaginary == 0.0) {<a name="line.122"></a>
<FONT color="green">123</FONT>                    return Math.abs(real);<a name="line.123"></a>
<FONT color="green">124</FONT>                }<a name="line.124"></a>
<FONT color="green">125</FONT>                double q = real / imaginary;<a name="line.125"></a>
<FONT color="green">126</FONT>                return (Math.abs(imaginary) * Math.sqrt(1 + q*q));<a name="line.126"></a>
<FONT color="green">127</FONT>            } else {<a name="line.127"></a>
<FONT color="green">128</FONT>                if (real == 0.0) {<a name="line.128"></a>
<FONT color="green">129</FONT>                    return Math.abs(imaginary);<a name="line.129"></a>
<FONT color="green">130</FONT>                }<a name="line.130"></a>
<FONT color="green">131</FONT>                double q = imaginary / real;<a name="line.131"></a>
<FONT color="green">132</FONT>                return (Math.abs(real) * Math.sqrt(1 + q*q));<a name="line.132"></a>
<FONT color="green">133</FONT>            }<a name="line.133"></a>
<FONT color="green">134</FONT>        }<a name="line.134"></a>
<FONT color="green">135</FONT>        <a name="line.135"></a>
<FONT color="green">136</FONT>        /**<a name="line.136"></a>
<FONT color="green">137</FONT>         * Return the sum of this complex number and the given complex number.<a name="line.137"></a>
<FONT color="green">138</FONT>         * &lt;p&gt;<a name="line.138"></a>
<FONT color="green">139</FONT>         * Uses the definitional formula <a name="line.139"></a>
<FONT color="green">140</FONT>         * &lt;pre&gt;<a name="line.140"></a>
<FONT color="green">141</FONT>         * (a + bi) + (c + di) = (a+c) + (b+d)i<a name="line.141"></a>
<FONT color="green">142</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.142"></a>
<FONT color="green">143</FONT>         * &lt;p&gt;<a name="line.143"></a>
<FONT color="green">144</FONT>         * If either this or &lt;code&gt;rhs&lt;/code&gt; has a NaN value in either part,<a name="line.144"></a>
<FONT color="green">145</FONT>         * {@link #NaN} is returned; otherwise Inifinite and NaN values are<a name="line.145"></a>
<FONT color="green">146</FONT>         * returned in the parts of the result according to the rules for<a name="line.146"></a>
<FONT color="green">147</FONT>         * {@link java.lang.Double} arithmetic.&lt;/p&gt; <a name="line.147"></a>
<FONT color="green">148</FONT>         *<a name="line.148"></a>
<FONT color="green">149</FONT>         * @param rhs the other complex number<a name="line.149"></a>
<FONT color="green">150</FONT>         * @return the complex number sum<a name="line.150"></a>
<FONT color="green">151</FONT>         * @throws NullPointerException if &lt;code&gt;rhs&lt;/code&gt; is null<a name="line.151"></a>
<FONT color="green">152</FONT>         */<a name="line.152"></a>
<FONT color="green">153</FONT>        public Complex add(Complex rhs) {   <a name="line.153"></a>
<FONT color="green">154</FONT>            return createComplex(real + rhs.getReal(),<a name="line.154"></a>
<FONT color="green">155</FONT>                imaginary + rhs.getImaginary());<a name="line.155"></a>
<FONT color="green">156</FONT>        }<a name="line.156"></a>
<FONT color="green">157</FONT>        <a name="line.157"></a>
<FONT color="green">158</FONT>        /**<a name="line.158"></a>
<FONT color="green">159</FONT>         * Return the conjugate of this complex number. The conjugate of<a name="line.159"></a>
<FONT color="green">160</FONT>         * "A + Bi" is "A - Bi". <a name="line.160"></a>
<FONT color="green">161</FONT>         * &lt;p&gt;<a name="line.161"></a>
<FONT color="green">162</FONT>         * {@link #NaN} is returned if either the real or imaginary<a name="line.162"></a>
<FONT color="green">163</FONT>         * part of this Complex number equals &lt;code&gt;Double.NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.163"></a>
<FONT color="green">164</FONT>         * &lt;p&gt;<a name="line.164"></a>
<FONT color="green">165</FONT>         * If the imaginary part is infinite, and the real part is not NaN, <a name="line.165"></a>
<FONT color="green">166</FONT>         * the returned value has infinite imaginary part of the opposite<a name="line.166"></a>
<FONT color="green">167</FONT>         * sign - e.g. the conjugate of &lt;code&gt;1 + POSITIVE_INFINITY i&lt;/code&gt;<a name="line.167"></a>
<FONT color="green">168</FONT>         * is &lt;code&gt;1 - NEGATIVE_INFINITY i&lt;/code&gt;&lt;/p&gt;<a name="line.168"></a>
<FONT color="green">169</FONT>         *<a name="line.169"></a>
<FONT color="green">170</FONT>         * @return the conjugate of this Complex object<a name="line.170"></a>
<FONT color="green">171</FONT>         */<a name="line.171"></a>
<FONT color="green">172</FONT>        public Complex conjugate() {<a name="line.172"></a>
<FONT color="green">173</FONT>            if (isNaN()) {<a name="line.173"></a>
<FONT color="green">174</FONT>                return NaN;<a name="line.174"></a>
<FONT color="green">175</FONT>            }   <a name="line.175"></a>
<FONT color="green">176</FONT>            return createComplex(real, -imaginary);<a name="line.176"></a>
<FONT color="green">177</FONT>        }<a name="line.177"></a>
<FONT color="green">178</FONT>        <a name="line.178"></a>
<FONT color="green">179</FONT>        /**<a name="line.179"></a>
<FONT color="green">180</FONT>         * Return the quotient of this complex number and the given complex number.<a name="line.180"></a>
<FONT color="green">181</FONT>         * &lt;p&gt;<a name="line.181"></a>
<FONT color="green">182</FONT>         * Implements the definitional formula<a name="line.182"></a>
<FONT color="green">183</FONT>         * &lt;pre&gt;&lt;code&gt;<a name="line.183"></a>
<FONT color="green">184</FONT>         *    a + bi          ac + bd + (bc - ad)i<a name="line.184"></a>
<FONT color="green">185</FONT>         *    ----------- = -------------------------<a name="line.185"></a>
<FONT color="green">186</FONT>         *    c + di               c&lt;sup&gt;2&lt;/sup&gt; + d&lt;sup&gt;2&lt;/sup&gt;<a name="line.186"></a>
<FONT color="green">187</FONT>         * &lt;/code&gt;&lt;/pre&gt;<a name="line.187"></a>
<FONT color="green">188</FONT>         * but uses <a name="line.188"></a>
<FONT color="green">189</FONT>         * &lt;a href="http://doi.acm.org/10.1145/1039813.1039814"&gt;<a name="line.189"></a>
<FONT color="green">190</FONT>         * prescaling of operands&lt;/a&gt; to limit the effects of overflows and<a name="line.190"></a>
<FONT color="green">191</FONT>         * underflows in the computation.&lt;/p&gt;<a name="line.191"></a>
<FONT color="green">192</FONT>         * &lt;p&gt;<a name="line.192"></a>
<FONT color="green">193</FONT>         * Infinite and NaN values are handled / returned according to the<a name="line.193"></a>
<FONT color="green">194</FONT>         * following rules, applied in the order presented:<a name="line.194"></a>
<FONT color="green">195</FONT>         * &lt;ul&gt;<a name="line.195"></a>
<FONT color="green">196</FONT>         * &lt;li&gt;If either this or &lt;code&gt;rhs&lt;/code&gt; has a NaN value in either part,<a name="line.196"></a>
<FONT color="green">197</FONT>         *  {@link #NaN} is returned.&lt;/li&gt;<a name="line.197"></a>
<FONT color="green">198</FONT>         * &lt;li&gt;If &lt;code&gt;rhs&lt;/code&gt; equals {@link #ZERO}, {@link #NaN} is returned.<a name="line.198"></a>
<FONT color="green">199</FONT>         * &lt;/li&gt;<a name="line.199"></a>
<FONT color="green">200</FONT>         * &lt;li&gt;If this and &lt;code&gt;rhs&lt;/code&gt; are both infinite,<a name="line.200"></a>
<FONT color="green">201</FONT>         * {@link #NaN} is returned.&lt;/li&gt;<a name="line.201"></a>
<FONT color="green">202</FONT>         * &lt;li&gt;If this is finite (i.e., has no infinite or NaN parts) and<a name="line.202"></a>
<FONT color="green">203</FONT>         *  &lt;code&gt;rhs&lt;/code&gt; is infinite (one or both parts infinite), <a name="line.203"></a>
<FONT color="green">204</FONT>         * {@link #ZERO} is returned.&lt;/li&gt;<a name="line.204"></a>
<FONT color="green">205</FONT>         * &lt;li&gt;If this is infinite and &lt;code&gt;rhs&lt;/code&gt; is finite, NaN values are<a name="line.205"></a>
<FONT color="green">206</FONT>         * returned in the parts of the result if the {@link java.lang.Double}<a name="line.206"></a>
<FONT color="green">207</FONT>         * rules applied to the definitional formula force NaN results.&lt;/li&gt;<a name="line.207"></a>
<FONT color="green">208</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.208"></a>
<FONT color="green">209</FONT>         * <a name="line.209"></a>
<FONT color="green">210</FONT>         * @param rhs the other complex number<a name="line.210"></a>
<FONT color="green">211</FONT>         * @return the complex number quotient<a name="line.211"></a>
<FONT color="green">212</FONT>         * @throws NullPointerException if &lt;code&gt;rhs&lt;/code&gt; is null<a name="line.212"></a>
<FONT color="green">213</FONT>         */<a name="line.213"></a>
<FONT color="green">214</FONT>        public Complex divide(Complex rhs) {<a name="line.214"></a>
<FONT color="green">215</FONT>            if (isNaN() || rhs.isNaN()) {<a name="line.215"></a>
<FONT color="green">216</FONT>                return NaN;<a name="line.216"></a>
<FONT color="green">217</FONT>            }<a name="line.217"></a>
<FONT color="green">218</FONT>    <a name="line.218"></a>
<FONT color="green">219</FONT>            double c = rhs.getReal();<a name="line.219"></a>
<FONT color="green">220</FONT>            double d = rhs.getImaginary();<a name="line.220"></a>
<FONT color="green">221</FONT>            if (c == 0.0 &amp;&amp; d == 0.0) {<a name="line.221"></a>
<FONT color="green">222</FONT>                return NaN;<a name="line.222"></a>
<FONT color="green">223</FONT>            }<a name="line.223"></a>
<FONT color="green">224</FONT>            <a name="line.224"></a>
<FONT color="green">225</FONT>            if (rhs.isInfinite() &amp;&amp; !isInfinite()) {<a name="line.225"></a>
<FONT color="green">226</FONT>                return ZERO;<a name="line.226"></a>
<FONT color="green">227</FONT>            }<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>            if (Math.abs(c) &lt; Math.abs(d)) {<a name="line.229"></a>
<FONT color="green">230</FONT>                if (d == 0.0) {<a name="line.230"></a>
<FONT color="green">231</FONT>                    return createComplex(real/c, imaginary/c);<a name="line.231"></a>
<FONT color="green">232</FONT>                }<a name="line.232"></a>
<FONT color="green">233</FONT>                double q = c / d;<a name="line.233"></a>
<FONT color="green">234</FONT>                double denominator = c * q + d;<a name="line.234"></a>
<FONT color="green">235</FONT>                return createComplex((real * q + imaginary) / denominator,<a name="line.235"></a>
<FONT color="green">236</FONT>                    (imaginary * q - real) / denominator);<a name="line.236"></a>
<FONT color="green">237</FONT>            } else {<a name="line.237"></a>
<FONT color="green">238</FONT>                if (c == 0.0) {<a name="line.238"></a>
<FONT color="green">239</FONT>                    return createComplex(imaginary/d, -real/c);<a name="line.239"></a>
<FONT color="green">240</FONT>                }<a name="line.240"></a>
<FONT color="green">241</FONT>                double q = d / c;<a name="line.241"></a>
<FONT color="green">242</FONT>                double denominator = d * q + c;<a name="line.242"></a>
<FONT color="green">243</FONT>                return createComplex((imaginary * q + real) / denominator,<a name="line.243"></a>
<FONT color="green">244</FONT>                    (imaginary - real * q) / denominator);<a name="line.244"></a>
<FONT color="green">245</FONT>            }<a name="line.245"></a>
<FONT color="green">246</FONT>        }<a name="line.246"></a>
<FONT color="green">247</FONT>        <a name="line.247"></a>
<FONT color="green">248</FONT>        /**<a name="line.248"></a>
<FONT color="green">249</FONT>         * Test for the equality of two Complex objects.<a name="line.249"></a>
<FONT color="green">250</FONT>         * &lt;p&gt;<a name="line.250"></a>
<FONT color="green">251</FONT>         * If both the real and imaginary parts of two Complex numbers<a name="line.251"></a>
<FONT color="green">252</FONT>         * are exactly the same, and neither is &lt;code&gt;Double.NaN&lt;/code&gt;, the two<a name="line.252"></a>
<FONT color="green">253</FONT>         * Complex objects are considered to be equal.&lt;/p&gt;<a name="line.253"></a>
<FONT color="green">254</FONT>         * &lt;p&gt;<a name="line.254"></a>
<FONT color="green">255</FONT>         * All &lt;code&gt;NaN&lt;/code&gt; values are considered to be equal - i.e, if either<a name="line.255"></a>
<FONT color="green">256</FONT>         * (or both) real and imaginary parts of the complex number are equal<a name="line.256"></a>
<FONT color="green">257</FONT>         * to &lt;code&gt;Double.NaN&lt;/code&gt;, the complex number is equal to <a name="line.257"></a>
<FONT color="green">258</FONT>         * &lt;code&gt;Complex.NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.258"></a>
<FONT color="green">259</FONT>         *<a name="line.259"></a>
<FONT color="green">260</FONT>         * @param other Object to test for equality to this<a name="line.260"></a>
<FONT color="green">261</FONT>         * @return true if two Complex objects are equal, false if<a name="line.261"></a>
<FONT color="green">262</FONT>         *         object is null, not an instance of Complex, or<a name="line.262"></a>
<FONT color="green">263</FONT>         *         not equal to this Complex instance<a name="line.263"></a>
<FONT color="green">264</FONT>         * <a name="line.264"></a>
<FONT color="green">265</FONT>         */<a name="line.265"></a>
<FONT color="green">266</FONT>        @Override<a name="line.266"></a>
<FONT color="green">267</FONT>        public boolean equals(Object other) {<a name="line.267"></a>
<FONT color="green">268</FONT>            boolean ret;<a name="line.268"></a>
<FONT color="green">269</FONT>            <a name="line.269"></a>
<FONT color="green">270</FONT>            if (this == other) { <a name="line.270"></a>
<FONT color="green">271</FONT>                ret = true;<a name="line.271"></a>
<FONT color="green">272</FONT>            } else if (other == null) {<a name="line.272"></a>
<FONT color="green">273</FONT>                ret = false;<a name="line.273"></a>
<FONT color="green">274</FONT>            } else  {<a name="line.274"></a>
<FONT color="green">275</FONT>                try {<a name="line.275"></a>
<FONT color="green">276</FONT>                    Complex rhs = (Complex)other;<a name="line.276"></a>
<FONT color="green">277</FONT>                    if (rhs.isNaN()) {<a name="line.277"></a>
<FONT color="green">278</FONT>                        ret = this.isNaN();<a name="line.278"></a>
<FONT color="green">279</FONT>                    } else {<a name="line.279"></a>
<FONT color="green">280</FONT>                        ret = (real == rhs.real) &amp;&amp; (imaginary == rhs.imaginary); <a name="line.280"></a>
<FONT color="green">281</FONT>                    }<a name="line.281"></a>
<FONT color="green">282</FONT>                } catch (ClassCastException ex) {<a name="line.282"></a>
<FONT color="green">283</FONT>                    // ignore exception<a name="line.283"></a>
<FONT color="green">284</FONT>                    ret = false;<a name="line.284"></a>
<FONT color="green">285</FONT>                }<a name="line.285"></a>
<FONT color="green">286</FONT>            }<a name="line.286"></a>
<FONT color="green">287</FONT>          <a name="line.287"></a>
<FONT color="green">288</FONT>            return ret;<a name="line.288"></a>
<FONT color="green">289</FONT>        }<a name="line.289"></a>
<FONT color="green">290</FONT>        <a name="line.290"></a>
<FONT color="green">291</FONT>        /**<a name="line.291"></a>
<FONT color="green">292</FONT>         * Get a hashCode for the complex number.<a name="line.292"></a>
<FONT color="green">293</FONT>         * &lt;p&gt;<a name="line.293"></a>
<FONT color="green">294</FONT>         * All NaN values have the same hash code.&lt;/p&gt;<a name="line.294"></a>
<FONT color="green">295</FONT>         * <a name="line.295"></a>
<FONT color="green">296</FONT>         * @return a hash code value for this object<a name="line.296"></a>
<FONT color="green">297</FONT>         */<a name="line.297"></a>
<FONT color="green">298</FONT>        @Override<a name="line.298"></a>
<FONT color="green">299</FONT>        public int hashCode() {<a name="line.299"></a>
<FONT color="green">300</FONT>            if (isNaN()) {<a name="line.300"></a>
<FONT color="green">301</FONT>                return 7;<a name="line.301"></a>
<FONT color="green">302</FONT>            }<a name="line.302"></a>
<FONT color="green">303</FONT>            return 37 * (17 * MathUtils.hash(imaginary) + <a name="line.303"></a>
<FONT color="green">304</FONT>                MathUtils.hash(real));<a name="line.304"></a>
<FONT color="green">305</FONT>        }<a name="line.305"></a>
<FONT color="green">306</FONT>    <a name="line.306"></a>
<FONT color="green">307</FONT>        /**<a name="line.307"></a>
<FONT color="green">308</FONT>         * Access the imaginary part.<a name="line.308"></a>
<FONT color="green">309</FONT>         *<a name="line.309"></a>
<FONT color="green">310</FONT>         * @return the imaginary part<a name="line.310"></a>
<FONT color="green">311</FONT>         */<a name="line.311"></a>
<FONT color="green">312</FONT>        public double getImaginary() {<a name="line.312"></a>
<FONT color="green">313</FONT>            return imaginary;<a name="line.313"></a>
<FONT color="green">314</FONT>        }<a name="line.314"></a>
<FONT color="green">315</FONT>    <a name="line.315"></a>
<FONT color="green">316</FONT>        /**<a name="line.316"></a>
<FONT color="green">317</FONT>         * Access the real part.<a name="line.317"></a>
<FONT color="green">318</FONT>         *<a name="line.318"></a>
<FONT color="green">319</FONT>         * @return the real part<a name="line.319"></a>
<FONT color="green">320</FONT>         */<a name="line.320"></a>
<FONT color="green">321</FONT>        public double getReal() {<a name="line.321"></a>
<FONT color="green">322</FONT>            return real;<a name="line.322"></a>
<FONT color="green">323</FONT>        }<a name="line.323"></a>
<FONT color="green">324</FONT>        <a name="line.324"></a>
<FONT color="green">325</FONT>        /**<a name="line.325"></a>
<FONT color="green">326</FONT>         * Returns true if either or both parts of this complex number is NaN;<a name="line.326"></a>
<FONT color="green">327</FONT>         * false otherwise<a name="line.327"></a>
<FONT color="green">328</FONT>         *<a name="line.328"></a>
<FONT color="green">329</FONT>         * @return  true if either or both parts of this complex number is NaN;<a name="line.329"></a>
<FONT color="green">330</FONT>         * false otherwise<a name="line.330"></a>
<FONT color="green">331</FONT>         */<a name="line.331"></a>
<FONT color="green">332</FONT>        public boolean isNaN() {<a name="line.332"></a>
<FONT color="green">333</FONT>            return isNaN;        <a name="line.333"></a>
<FONT color="green">334</FONT>        }<a name="line.334"></a>
<FONT color="green">335</FONT>        <a name="line.335"></a>
<FONT color="green">336</FONT>        /**<a name="line.336"></a>
<FONT color="green">337</FONT>         * Returns true if either the real or imaginary part of this complex number<a name="line.337"></a>
<FONT color="green">338</FONT>         * takes an infinite value (either &lt;code&gt;Double.POSITIVE_INFINITY&lt;/code&gt; or <a name="line.338"></a>
<FONT color="green">339</FONT>         * &lt;code&gt;Double.NEGATIVE_INFINITY&lt;/code&gt;) and neither part<a name="line.339"></a>
<FONT color="green">340</FONT>         * is &lt;code&gt;NaN&lt;/code&gt;.<a name="line.340"></a>
<FONT color="green">341</FONT>         * <a name="line.341"></a>
<FONT color="green">342</FONT>         * @return true if one or both parts of this complex number are infinite<a name="line.342"></a>
<FONT color="green">343</FONT>         * and neither part is &lt;code&gt;NaN&lt;/code&gt;<a name="line.343"></a>
<FONT color="green">344</FONT>         */<a name="line.344"></a>
<FONT color="green">345</FONT>        public boolean isInfinite() {<a name="line.345"></a>
<FONT color="green">346</FONT>            return isInfinite;        <a name="line.346"></a>
<FONT color="green">347</FONT>        }<a name="line.347"></a>
<FONT color="green">348</FONT>        <a name="line.348"></a>
<FONT color="green">349</FONT>        /**<a name="line.349"></a>
<FONT color="green">350</FONT>         * Return the product of this complex number and the given complex number.<a name="line.350"></a>
<FONT color="green">351</FONT>         * &lt;p&gt;<a name="line.351"></a>
<FONT color="green">352</FONT>         * Implements preliminary checks for NaN and infinity followed by<a name="line.352"></a>
<FONT color="green">353</FONT>         * the definitional formula:<a name="line.353"></a>
<FONT color="green">354</FONT>         * &lt;pre&gt;&lt;code&gt;<a name="line.354"></a>
<FONT color="green">355</FONT>         * (a + bi)(c + di) = (ac - bd) + (ad + bc)i<a name="line.355"></a>
<FONT color="green">356</FONT>         * &lt;/code&gt;&lt;/pre&gt;<a name="line.356"></a>
<FONT color="green">357</FONT>         * &lt;/p&gt;<a name="line.357"></a>
<FONT color="green">358</FONT>         * &lt;p&gt;<a name="line.358"></a>
<FONT color="green">359</FONT>         * Returns {@link #NaN} if either this or &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.359"></a>
<FONT color="green">360</FONT>         * NaN parts.<a name="line.360"></a>
<FONT color="green">361</FONT>         * &lt;/p&gt;<a name="line.361"></a>
<FONT color="green">362</FONT>         * Returns {@link #INF} if neither this nor &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.362"></a>
<FONT color="green">363</FONT>         * NaN parts and if either this or &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.363"></a>
<FONT color="green">364</FONT>         * infinite parts (same result is returned regardless of the sign of the<a name="line.364"></a>
<FONT color="green">365</FONT>         * components).<a name="line.365"></a>
<FONT color="green">366</FONT>         * &lt;/p&gt;<a name="line.366"></a>
<FONT color="green">367</FONT>         * &lt;p&gt;<a name="line.367"></a>
<FONT color="green">368</FONT>         * Returns finite values in components of the result per the<a name="line.368"></a>
<FONT color="green">369</FONT>         * definitional formula in all remaining cases.<a name="line.369"></a>
<FONT color="green">370</FONT>         *  &lt;/p&gt;<a name="line.370"></a>
<FONT color="green">371</FONT>         * <a name="line.371"></a>
<FONT color="green">372</FONT>         * @param rhs the other complex number<a name="line.372"></a>
<FONT color="green">373</FONT>         * @return the complex number product<a name="line.373"></a>
<FONT color="green">374</FONT>         * @throws NullPointerException if &lt;code&gt;rhs&lt;/code&gt; is null<a name="line.374"></a>
<FONT color="green">375</FONT>         */<a name="line.375"></a>
<FONT color="green">376</FONT>        public Complex multiply(Complex rhs) {<a name="line.376"></a>
<FONT color="green">377</FONT>            if (isNaN() || rhs.isNaN()) {<a name="line.377"></a>
<FONT color="green">378</FONT>                return NaN;<a name="line.378"></a>
<FONT color="green">379</FONT>            }<a name="line.379"></a>
<FONT color="green">380</FONT>            if (Double.isInfinite(real) || Double.isInfinite(imaginary) ||<a name="line.380"></a>
<FONT color="green">381</FONT>                Double.isInfinite(rhs.real)|| Double.isInfinite(rhs.imaginary)) {<a name="line.381"></a>
<FONT color="green">382</FONT>                // we don't use Complex.isInfinite() to avoid testing for NaN again<a name="line.382"></a>
<FONT color="green">383</FONT>                return INF;<a name="line.383"></a>
<FONT color="green">384</FONT>            }<a name="line.384"></a>
<FONT color="green">385</FONT>            return createComplex(real * rhs.real - imaginary * rhs.imaginary,<a name="line.385"></a>
<FONT color="green">386</FONT>                    real * rhs.imaginary + imaginary * rhs.real);<a name="line.386"></a>
<FONT color="green">387</FONT>        }<a name="line.387"></a>
<FONT color="green">388</FONT>        <a name="line.388"></a>
<FONT color="green">389</FONT>        /**<a name="line.389"></a>
<FONT color="green">390</FONT>         * Return the product of this complex number and the given scalar number.<a name="line.390"></a>
<FONT color="green">391</FONT>         * &lt;p&gt;<a name="line.391"></a>
<FONT color="green">392</FONT>         * Implements preliminary checks for NaN and infinity followed by<a name="line.392"></a>
<FONT color="green">393</FONT>         * the definitional formula:<a name="line.393"></a>
<FONT color="green">394</FONT>         * &lt;pre&gt;&lt;code&gt;<a name="line.394"></a>
<FONT color="green">395</FONT>         * c(a + bi) = (ca) + (cb)i<a name="line.395"></a>
<FONT color="green">396</FONT>         * &lt;/code&gt;&lt;/pre&gt;<a name="line.396"></a>
<FONT color="green">397</FONT>         * &lt;/p&gt;<a name="line.397"></a>
<FONT color="green">398</FONT>         * &lt;p&gt;<a name="line.398"></a>
<FONT color="green">399</FONT>         * Returns {@link #NaN} if either this or &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.399"></a>
<FONT color="green">400</FONT>         * NaN parts.<a name="line.400"></a>
<FONT color="green">401</FONT>         * &lt;/p&gt;<a name="line.401"></a>
<FONT color="green">402</FONT>         * Returns {@link #INF} if neither this nor &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.402"></a>
<FONT color="green">403</FONT>         * NaN parts and if either this or &lt;code&gt;rhs&lt;/code&gt; has one or more<a name="line.403"></a>
<FONT color="green">404</FONT>         * infinite parts (same result is returned regardless of the sign of the<a name="line.404"></a>
<FONT color="green">405</FONT>         * components).<a name="line.405"></a>
<FONT color="green">406</FONT>         * &lt;/p&gt;<a name="line.406"></a>
<FONT color="green">407</FONT>         * &lt;p&gt;<a name="line.407"></a>
<FONT color="green">408</FONT>         * Returns finite values in components of the result per the<a name="line.408"></a>
<FONT color="green">409</FONT>         * definitional formula in all remaining cases.<a name="line.409"></a>
<FONT color="green">410</FONT>         *  &lt;/p&gt;<a name="line.410"></a>
<FONT color="green">411</FONT>         * <a name="line.411"></a>
<FONT color="green">412</FONT>         * @param rhs the scalar number<a name="line.412"></a>
<FONT color="green">413</FONT>         * @return the complex number product<a name="line.413"></a>
<FONT color="green">414</FONT>         */<a name="line.414"></a>
<FONT color="green">415</FONT>        public Complex multiply(double rhs) {<a name="line.415"></a>
<FONT color="green">416</FONT>            if (isNaN() || Double.isNaN(rhs)) {<a name="line.416"></a>
<FONT color="green">417</FONT>                return NaN;<a name="line.417"></a>
<FONT color="green">418</FONT>            }<a name="line.418"></a>
<FONT color="green">419</FONT>            if (Double.isInfinite(real) || Double.isInfinite(imaginary) ||<a name="line.419"></a>
<FONT color="green">420</FONT>                Double.isInfinite(rhs)) {<a name="line.420"></a>
<FONT color="green">421</FONT>                // we don't use Complex.isInfinite() to avoid testing for NaN again<a name="line.421"></a>
<FONT color="green">422</FONT>                return INF;<a name="line.422"></a>
<FONT color="green">423</FONT>            }<a name="line.423"></a>
<FONT color="green">424</FONT>            return createComplex(real * rhs, imaginary * rhs);<a name="line.424"></a>
<FONT color="green">425</FONT>        }<a name="line.425"></a>
<FONT color="green">426</FONT>        <a name="line.426"></a>
<FONT color="green">427</FONT>        /**<a name="line.427"></a>
<FONT color="green">428</FONT>         * Return the additive inverse of this complex number.<a name="line.428"></a>
<FONT color="green">429</FONT>         * &lt;p&gt;<a name="line.429"></a>
<FONT color="green">430</FONT>         * Returns &lt;code&gt;Complex.NaN&lt;/code&gt; if either real or imaginary<a name="line.430"></a>
<FONT color="green">431</FONT>         * part of this Complex number equals &lt;code&gt;Double.NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.431"></a>
<FONT color="green">432</FONT>         *<a name="line.432"></a>
<FONT color="green">433</FONT>         * @return the negation of this complex number<a name="line.433"></a>
<FONT color="green">434</FONT>         */<a name="line.434"></a>
<FONT color="green">435</FONT>        public Complex negate() {<a name="line.435"></a>
<FONT color="green">436</FONT>            if (isNaN()) {<a name="line.436"></a>
<FONT color="green">437</FONT>                return NaN;<a name="line.437"></a>
<FONT color="green">438</FONT>            }<a name="line.438"></a>
<FONT color="green">439</FONT>            <a name="line.439"></a>
<FONT color="green">440</FONT>            return createComplex(-real, -imaginary);<a name="line.440"></a>
<FONT color="green">441</FONT>        }<a name="line.441"></a>
<FONT color="green">442</FONT>        <a name="line.442"></a>
<FONT color="green">443</FONT>        /**<a name="line.443"></a>
<FONT color="green">444</FONT>         * Return the difference between this complex number and the given complex<a name="line.444"></a>
<FONT color="green">445</FONT>         * number.<a name="line.445"></a>
<FONT color="green">446</FONT>          * &lt;p&gt;<a name="line.446"></a>
<FONT color="green">447</FONT>         * Uses the definitional formula <a name="line.447"></a>
<FONT color="green">448</FONT>         * &lt;pre&gt;<a name="line.448"></a>
<FONT color="green">449</FONT>         * (a + bi) - (c + di) = (a-c) + (b-d)i<a name="line.449"></a>
<FONT color="green">450</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.450"></a>
<FONT color="green">451</FONT>         * &lt;p&gt;<a name="line.451"></a>
<FONT color="green">452</FONT>         * If either this or &lt;code&gt;rhs&lt;/code&gt; has a NaN value in either part,<a name="line.452"></a>
<FONT color="green">453</FONT>         * {@link #NaN} is returned; otherwise inifinite and NaN values are<a name="line.453"></a>
<FONT color="green">454</FONT>         * returned in the parts of the result according to the rules for<a name="line.454"></a>
<FONT color="green">455</FONT>         * {@link java.lang.Double} arithmetic. &lt;/p&gt;<a name="line.455"></a>
<FONT color="green">456</FONT>         * <a name="line.456"></a>
<FONT color="green">457</FONT>         * @param rhs the other complex number<a name="line.457"></a>
<FONT color="green">458</FONT>         * @return the complex number difference<a name="line.458"></a>
<FONT color="green">459</FONT>         * @throws NullPointerException if &lt;code&gt;rhs&lt;/code&gt; is null<a name="line.459"></a>
<FONT color="green">460</FONT>         */<a name="line.460"></a>
<FONT color="green">461</FONT>        public Complex subtract(Complex rhs) {<a name="line.461"></a>
<FONT color="green">462</FONT>            if (isNaN() || rhs.isNaN()) {<a name="line.462"></a>
<FONT color="green">463</FONT>                return NaN;<a name="line.463"></a>
<FONT color="green">464</FONT>            }<a name="line.464"></a>
<FONT color="green">465</FONT>            <a name="line.465"></a>
<FONT color="green">466</FONT>            return createComplex(real - rhs.getReal(),<a name="line.466"></a>
<FONT color="green">467</FONT>                imaginary - rhs.getImaginary());<a name="line.467"></a>
<FONT color="green">468</FONT>        }<a name="line.468"></a>
<FONT color="green">469</FONT>        <a name="line.469"></a>
<FONT color="green">470</FONT>        /**<a name="line.470"></a>
<FONT color="green">471</FONT>         * Compute the <a name="line.471"></a>
<FONT color="green">472</FONT>         * &lt;a href="http://mathworld.wolfram.com/InverseCosine.html" TARGET="_top"&gt;<a name="line.472"></a>
<FONT color="green">473</FONT>         * inverse cosine&lt;/a&gt; of this complex number.<a name="line.473"></a>
<FONT color="green">474</FONT>         * &lt;p&gt;<a name="line.474"></a>
<FONT color="green">475</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.475"></a>
<FONT color="green">476</FONT>         * &lt;code&gt; acos(z) = -i (log(z + i (sqrt(1 - z&lt;sup&gt;2&lt;/sup&gt;))))&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.476"></a>
<FONT color="green">477</FONT>         * &lt;p&gt;<a name="line.477"></a>
<FONT color="green">478</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.478"></a>
<FONT color="green">479</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt; or infinite.&lt;/p&gt;<a name="line.479"></a>
<FONT color="green">480</FONT>         * <a name="line.480"></a>
<FONT color="green">481</FONT>         * @return the inverse cosine of this complex number<a name="line.481"></a>
<FONT color="green">482</FONT>         * @since 1.2<a name="line.482"></a>
<FONT color="green">483</FONT>         */<a name="line.483"></a>
<FONT color="green">484</FONT>        public Complex acos() {<a name="line.484"></a>
<FONT color="green">485</FONT>            if (isNaN()) {<a name="line.485"></a>
<FONT color="green">486</FONT>                return Complex.NaN;<a name="line.486"></a>
<FONT color="green">487</FONT>            }<a name="line.487"></a>
<FONT color="green">488</FONT>    <a name="line.488"></a>
<FONT color="green">489</FONT>            return this.add(this.sqrt1z().multiply(Complex.I)).log()<a name="line.489"></a>
<FONT color="green">490</FONT>                  .multiply(Complex.I.negate());<a name="line.490"></a>
<FONT color="green">491</FONT>        }<a name="line.491"></a>
<FONT color="green">492</FONT>        <a name="line.492"></a>
<FONT color="green">493</FONT>        /**<a name="line.493"></a>
<FONT color="green">494</FONT>         * Compute the <a name="line.494"></a>
<FONT color="green">495</FONT>         * &lt;a href="http://mathworld.wolfram.com/InverseSine.html" TARGET="_top"&gt;<a name="line.495"></a>
<FONT color="green">496</FONT>         * inverse sine&lt;/a&gt; of this complex number.<a name="line.496"></a>
<FONT color="green">497</FONT>         * &lt;p&gt;<a name="line.497"></a>
<FONT color="green">498</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.498"></a>
<FONT color="green">499</FONT>         * &lt;code&gt; asin(z) = -i (log(sqrt(1 - z&lt;sup&gt;2&lt;/sup&gt;) + iz)) &lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.499"></a>
<FONT color="green">500</FONT>         * &lt;p&gt;<a name="line.500"></a>
<FONT color="green">501</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.501"></a>
<FONT color="green">502</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt; or infinite.&lt;/p&gt;<a name="line.502"></a>
<FONT color="green">503</FONT>         * <a name="line.503"></a>
<FONT color="green">504</FONT>         * @return the inverse sine of this complex number.<a name="line.504"></a>
<FONT color="green">505</FONT>         * @since 1.2<a name="line.505"></a>
<FONT color="green">506</FONT>         */<a name="line.506"></a>
<FONT color="green">507</FONT>        public Complex asin() {<a name="line.507"></a>
<FONT color="green">508</FONT>            if (isNaN()) {<a name="line.508"></a>
<FONT color="green">509</FONT>                return Complex.NaN;<a name="line.509"></a>
<FONT color="green">510</FONT>            }<a name="line.510"></a>
<FONT color="green">511</FONT>    <a name="line.511"></a>
<FONT color="green">512</FONT>            return sqrt1z().add(this.multiply(Complex.I)).log()<a name="line.512"></a>
<FONT color="green">513</FONT>                  .multiply(Complex.I.negate());<a name="line.513"></a>
<FONT color="green">514</FONT>        }<a name="line.514"></a>
<FONT color="green">515</FONT>        <a name="line.515"></a>
<FONT color="green">516</FONT>        /**<a name="line.516"></a>
<FONT color="green">517</FONT>         * Compute the <a name="line.517"></a>
<FONT color="green">518</FONT>         * &lt;a href="http://mathworld.wolfram.com/InverseTangent.html" TARGET="_top"&gt;<a name="line.518"></a>
<FONT color="green">519</FONT>         * inverse tangent&lt;/a&gt; of this complex number.<a name="line.519"></a>
<FONT color="green">520</FONT>         * &lt;p&gt;<a name="line.520"></a>
<FONT color="green">521</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.521"></a>
<FONT color="green">522</FONT>         * &lt;code&gt; atan(z) = (i/2) log((i + z)/(i - z)) &lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.522"></a>
<FONT color="green">523</FONT>         * &lt;p&gt;<a name="line.523"></a>
<FONT color="green">524</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.524"></a>
<FONT color="green">525</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt; or infinite.&lt;/p&gt;<a name="line.525"></a>
<FONT color="green">526</FONT>         * <a name="line.526"></a>
<FONT color="green">527</FONT>         * @return the inverse tangent of this complex number<a name="line.527"></a>
<FONT color="green">528</FONT>         * @since 1.2<a name="line.528"></a>
<FONT color="green">529</FONT>         */<a name="line.529"></a>
<FONT color="green">530</FONT>        public Complex atan() {<a name="line.530"></a>
<FONT color="green">531</FONT>            if (isNaN()) {<a name="line.531"></a>
<FONT color="green">532</FONT>                return Complex.NaN;<a name="line.532"></a>
<FONT color="green">533</FONT>            }<a name="line.533"></a>
<FONT color="green">534</FONT>            <a name="line.534"></a>
<FONT color="green">535</FONT>            return this.add(Complex.I).divide(Complex.I.subtract(this)).log()<a name="line.535"></a>
<FONT color="green">536</FONT>                .multiply(Complex.I.divide(createComplex(2.0, 0.0)));<a name="line.536"></a>
<FONT color="green">537</FONT>        }<a name="line.537"></a>
<FONT color="green">538</FONT>        <a name="line.538"></a>
<FONT color="green">539</FONT>        /**<a name="line.539"></a>
<FONT color="green">540</FONT>         * Compute the <a name="line.540"></a>
<FONT color="green">541</FONT>         * &lt;a href="http://mathworld.wolfram.com/Cosine.html" TARGET="_top"&gt;<a name="line.541"></a>
<FONT color="green">542</FONT>         * cosine&lt;/a&gt;<a name="line.542"></a>
<FONT color="green">543</FONT>         * of this complex number.<a name="line.543"></a>
<FONT color="green">544</FONT>         * &lt;p&gt;<a name="line.544"></a>
<FONT color="green">545</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.545"></a>
<FONT color="green">546</FONT>         * &lt;code&gt; cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i&lt;/code&gt;&lt;/pre&gt;<a name="line.546"></a>
<FONT color="green">547</FONT>         * where the (real) functions on the right-hand side are<a name="line.547"></a>
<FONT color="green">548</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.548"></a>
<FONT color="green">549</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.549"></a>
<FONT color="green">550</FONT>         * &lt;p&gt;<a name="line.550"></a>
<FONT color="green">551</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.551"></a>
<FONT color="green">552</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.552"></a>
<FONT color="green">553</FONT>         * &lt;p&gt;<a name="line.553"></a>
<FONT color="green">554</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.554"></a>
<FONT color="green">555</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.555"></a>
<FONT color="green">556</FONT>         * Examples: <a name="line.556"></a>
<FONT color="green">557</FONT>         * &lt;code&gt;<a name="line.557"></a>
<FONT color="green">558</FONT>         * cos(1 &amp;plusmn; INFINITY i) = 1 &amp;#x2213; INFINITY i<a name="line.558"></a>
<FONT color="green">559</FONT>         * cos(&amp;plusmn;INFINITY + i) = NaN + NaN i<a name="line.559"></a>
<FONT color="green">560</FONT>         * cos(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.560"></a>
<FONT color="green">561</FONT>         * <a name="line.561"></a>
<FONT color="green">562</FONT>         * @return the cosine of this complex number<a name="line.562"></a>
<FONT color="green">563</FONT>         * @since 1.2<a name="line.563"></a>
<FONT color="green">564</FONT>         */<a name="line.564"></a>
<FONT color="green">565</FONT>        public Complex cos() {<a name="line.565"></a>
<FONT color="green">566</FONT>            if (isNaN()) {<a name="line.566"></a>
<FONT color="green">567</FONT>                return Complex.NaN;<a name="line.567"></a>
<FONT color="green">568</FONT>            }<a name="line.568"></a>
<FONT color="green">569</FONT>            <a name="line.569"></a>
<FONT color="green">570</FONT>            return createComplex(Math.cos(real) * MathUtils.cosh(imaginary),<a name="line.570"></a>
<FONT color="green">571</FONT>                -Math.sin(real) * MathUtils.sinh(imaginary));<a name="line.571"></a>
<FONT color="green">572</FONT>        }<a name="line.572"></a>
<FONT color="green">573</FONT>        <a name="line.573"></a>
<FONT color="green">574</FONT>        /**<a name="line.574"></a>
<FONT color="green">575</FONT>         * Compute the <a name="line.575"></a>
<FONT color="green">576</FONT>         * &lt;a href="http://mathworld.wolfram.com/HyperbolicCosine.html" TARGET="_top"&gt;<a name="line.576"></a>
<FONT color="green">577</FONT>         * hyperbolic cosine&lt;/a&gt; of this complex number.<a name="line.577"></a>
<FONT color="green">578</FONT>         * &lt;p&gt;<a name="line.578"></a>
<FONT color="green">579</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.579"></a>
<FONT color="green">580</FONT>         * &lt;code&gt; cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i&lt;/code&gt;&lt;/pre&gt;<a name="line.580"></a>
<FONT color="green">581</FONT>         * where the (real) functions on the right-hand side are<a name="line.581"></a>
<FONT color="green">582</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.582"></a>
<FONT color="green">583</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.583"></a>
<FONT color="green">584</FONT>         * &lt;p&gt;<a name="line.584"></a>
<FONT color="green">585</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.585"></a>
<FONT color="green">586</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.586"></a>
<FONT color="green">587</FONT>         * &lt;p&gt;<a name="line.587"></a>
<FONT color="green">588</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.588"></a>
<FONT color="green">589</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.589"></a>
<FONT color="green">590</FONT>         * Examples: <a name="line.590"></a>
<FONT color="green">591</FONT>         * &lt;code&gt;<a name="line.591"></a>
<FONT color="green">592</FONT>         * cosh(1 &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.592"></a>
<FONT color="green">593</FONT>         * cosh(&amp;plusmn;INFINITY + i) = INFINITY &amp;plusmn; INFINITY i<a name="line.593"></a>
<FONT color="green">594</FONT>         * cosh(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.594"></a>
<FONT color="green">595</FONT>         * <a name="line.595"></a>
<FONT color="green">596</FONT>         * @return the hyperbolic cosine of this complex number.<a name="line.596"></a>
<FONT color="green">597</FONT>         * @since 1.2<a name="line.597"></a>
<FONT color="green">598</FONT>         */<a name="line.598"></a>
<FONT color="green">599</FONT>        public Complex cosh() {<a name="line.599"></a>
<FONT color="green">600</FONT>            if (isNaN()) {<a name="line.600"></a>
<FONT color="green">601</FONT>                return Complex.NaN;<a name="line.601"></a>
<FONT color="green">602</FONT>            }<a name="line.602"></a>
<FONT color="green">603</FONT>            <a name="line.603"></a>
<FONT color="green">604</FONT>            return createComplex(MathUtils.cosh(real) * Math.cos(imaginary),<a name="line.604"></a>
<FONT color="green">605</FONT>                MathUtils.sinh(real) * Math.sin(imaginary));<a name="line.605"></a>
<FONT color="green">606</FONT>        }<a name="line.606"></a>
<FONT color="green">607</FONT>        <a name="line.607"></a>
<FONT color="green">608</FONT>        /**<a name="line.608"></a>
<FONT color="green">609</FONT>         * Compute the<a name="line.609"></a>
<FONT color="green">610</FONT>         * &lt;a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top"&gt;<a name="line.610"></a>
<FONT color="green">611</FONT>         * exponential function&lt;/a&gt; of this complex number.<a name="line.611"></a>
<FONT color="green">612</FONT>         * &lt;p&gt;<a name="line.612"></a>
<FONT color="green">613</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.613"></a>
<FONT color="green">614</FONT>         * &lt;code&gt; exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i&lt;/code&gt;&lt;/pre&gt;<a name="line.614"></a>
<FONT color="green">615</FONT>         * where the (real) functions on the right-hand side are<a name="line.615"></a>
<FONT color="green">616</FONT>         * {@link java.lang.Math#exp}, {@link java.lang.Math#cos}, and<a name="line.616"></a>
<FONT color="green">617</FONT>         * {@link java.lang.Math#sin}.&lt;/p&gt;<a name="line.617"></a>
<FONT color="green">618</FONT>         * &lt;p&gt;<a name="line.618"></a>
<FONT color="green">619</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.619"></a>
<FONT color="green">620</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.620"></a>
<FONT color="green">621</FONT>         * &lt;p&gt;<a name="line.621"></a>
<FONT color="green">622</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.622"></a>
<FONT color="green">623</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.623"></a>
<FONT color="green">624</FONT>         * Examples: <a name="line.624"></a>
<FONT color="green">625</FONT>         * &lt;code&gt;<a name="line.625"></a>
<FONT color="green">626</FONT>         * exp(1 &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.626"></a>
<FONT color="green">627</FONT>         * exp(INFINITY + i) = INFINITY + INFINITY i<a name="line.627"></a>
<FONT color="green">628</FONT>         * exp(-INFINITY + i) = 0 + 0i<a name="line.628"></a>
<FONT color="green">629</FONT>         * exp(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.629"></a>
<FONT color="green">630</FONT>         * <a name="line.630"></a>
<FONT color="green">631</FONT>         * @return &lt;i&gt;e&lt;/i&gt;&lt;sup&gt;&lt;code&gt;this&lt;/code&gt;&lt;/sup&gt;<a name="line.631"></a>
<FONT color="green">632</FONT>         * @since 1.2<a name="line.632"></a>
<FONT color="green">633</FONT>         */<a name="line.633"></a>
<FONT color="green">634</FONT>        public Complex exp() {<a name="line.634"></a>
<FONT color="green">635</FONT>            if (isNaN()) {<a name="line.635"></a>
<FONT color="green">636</FONT>                return Complex.NaN;<a name="line.636"></a>
<FONT color="green">637</FONT>            }<a name="line.637"></a>
<FONT color="green">638</FONT>            <a name="line.638"></a>
<FONT color="green">639</FONT>            double expReal = Math.exp(real);<a name="line.639"></a>
<FONT color="green">640</FONT>            return createComplex(expReal *  Math.cos(imaginary), expReal * Math.sin(imaginary));<a name="line.640"></a>
<FONT color="green">641</FONT>        }<a name="line.641"></a>
<FONT color="green">642</FONT>        <a name="line.642"></a>
<FONT color="green">643</FONT>        /**<a name="line.643"></a>
<FONT color="green">644</FONT>         * Compute the <a name="line.644"></a>
<FONT color="green">645</FONT>         * &lt;a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top"&gt;<a name="line.645"></a>
<FONT color="green">646</FONT>         * natural logarithm&lt;/a&gt; of this complex number.<a name="line.646"></a>
<FONT color="green">647</FONT>         * &lt;p&gt;<a name="line.647"></a>
<FONT color="green">648</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.648"></a>
<FONT color="green">649</FONT>         * &lt;code&gt; log(a + bi) = ln(|a + bi|) + arg(a + bi)i&lt;/code&gt;&lt;/pre&gt;<a name="line.649"></a>
<FONT color="green">650</FONT>         * where ln on the right hand side is {@link java.lang.Math#log},<a name="line.650"></a>
<FONT color="green">651</FONT>         * &lt;code&gt;|a + bi|&lt;/code&gt; is the modulus, {@link Complex#abs},  and<a name="line.651"></a>
<FONT color="green">652</FONT>         * &lt;code&gt;arg(a + bi) = {@link java.lang.Math#atan2}(b, a)&lt;/code&gt;&lt;/p&gt;<a name="line.652"></a>
<FONT color="green">653</FONT>         * &lt;p&gt;<a name="line.653"></a>
<FONT color="green">654</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.654"></a>
<FONT color="green">655</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.655"></a>
<FONT color="green">656</FONT>         * &lt;p&gt;<a name="line.656"></a>
<FONT color="green">657</FONT>         * Infinite (or critical) values in real or imaginary parts of the input may<a name="line.657"></a>
<FONT color="green">658</FONT>         * result in infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.658"></a>
<FONT color="green">659</FONT>         * Examples: <a name="line.659"></a>
<FONT color="green">660</FONT>         * &lt;code&gt;<a name="line.660"></a>
<FONT color="green">661</FONT>         * log(1 &amp;plusmn; INFINITY i) = INFINITY &amp;plusmn; (&amp;pi;/2)i<a name="line.661"></a>
<FONT color="green">662</FONT>         * log(INFINITY + i) = INFINITY + 0i<a name="line.662"></a>
<FONT color="green">663</FONT>         * log(-INFINITY + i) = INFINITY + &amp;pi;i<a name="line.663"></a>
<FONT color="green">664</FONT>         * log(INFINITY &amp;plusmn; INFINITY i) = INFINITY &amp;plusmn; (&amp;pi;/4)i<a name="line.664"></a>
<FONT color="green">665</FONT>         * log(-INFINITY &amp;plusmn; INFINITY i) = INFINITY &amp;plusmn; (3&amp;pi;/4)i<a name="line.665"></a>
<FONT color="green">666</FONT>         * log(0 + 0i) = -INFINITY + 0i<a name="line.666"></a>
<FONT color="green">667</FONT>         * &lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.667"></a>
<FONT color="green">668</FONT>         * <a name="line.668"></a>
<FONT color="green">669</FONT>         * @return ln of this complex number.<a name="line.669"></a>
<FONT color="green">670</FONT>         * @since 1.2<a name="line.670"></a>
<FONT color="green">671</FONT>         */<a name="line.671"></a>
<FONT color="green">672</FONT>        public Complex log() {<a name="line.672"></a>
<FONT color="green">673</FONT>            if (isNaN()) {<a name="line.673"></a>
<FONT color="green">674</FONT>                return Complex.NaN;<a name="line.674"></a>
<FONT color="green">675</FONT>            }<a name="line.675"></a>
<FONT color="green">676</FONT>    <a name="line.676"></a>
<FONT color="green">677</FONT>            return createComplex(Math.log(abs()),<a name="line.677"></a>
<FONT color="green">678</FONT>                Math.atan2(imaginary, real));        <a name="line.678"></a>
<FONT color="green">679</FONT>        }<a name="line.679"></a>
<FONT color="green">680</FONT>        <a name="line.680"></a>
<FONT color="green">681</FONT>        /**<a name="line.681"></a>
<FONT color="green">682</FONT>         * Returns of value of this complex number raised to the power of &lt;code&gt;x&lt;/code&gt;.<a name="line.682"></a>
<FONT color="green">683</FONT>         * &lt;p&gt;<a name="line.683"></a>
<FONT color="green">684</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.684"></a>
<FONT color="green">685</FONT>         * &lt;code&gt; y&lt;sup&gt;x&lt;/sup&gt; = exp(x&amp;middot;log(y))&lt;/code&gt;&lt;/pre&gt; <a name="line.685"></a>
<FONT color="green">686</FONT>         * where &lt;code&gt;exp&lt;/code&gt; and &lt;code&gt;log&lt;/code&gt; are {@link #exp} and<a name="line.686"></a>
<FONT color="green">687</FONT>         * {@link #log}, respectively.&lt;/p&gt;<a name="line.687"></a>
<FONT color="green">688</FONT>         * &lt;p&gt;<a name="line.688"></a>
<FONT color="green">689</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.689"></a>
<FONT color="green">690</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt; or infinite, or if &lt;code&gt;y&lt;/code&gt;<a name="line.690"></a>
<FONT color="green">691</FONT>         * equals {@link Complex#ZERO}.&lt;/p&gt;<a name="line.691"></a>
<FONT color="green">692</FONT>         * <a name="line.692"></a>
<FONT color="green">693</FONT>         * @param x the exponent.<a name="line.693"></a>
<FONT color="green">694</FONT>         * @return &lt;code&gt;this&lt;/code&gt;&lt;sup&gt;&lt;code&gt;x&lt;/code&gt;&lt;/sup&gt;<a name="line.694"></a>
<FONT color="green">695</FONT>         * @throws NullPointerException if x is null<a name="line.695"></a>
<FONT color="green">696</FONT>         * @since 1.2<a name="line.696"></a>
<FONT color="green">697</FONT>         */<a name="line.697"></a>
<FONT color="green">698</FONT>        public Complex pow(Complex x) {<a name="line.698"></a>
<FONT color="green">699</FONT>            if (x == null) {<a name="line.699"></a>
<FONT color="green">700</FONT>                throw new NullPointerException();<a name="line.700"></a>
<FONT color="green">701</FONT>            }<a name="line.701"></a>
<FONT color="green">702</FONT>            return this.log().multiply(x).exp();<a name="line.702"></a>
<FONT color="green">703</FONT>        }<a name="line.703"></a>
<FONT color="green">704</FONT>        <a name="line.704"></a>
<FONT color="green">705</FONT>        /**<a name="line.705"></a>
<FONT color="green">706</FONT>         * Compute the <a name="line.706"></a>
<FONT color="green">707</FONT>         * &lt;a href="http://mathworld.wolfram.com/Sine.html" TARGET="_top"&gt;<a name="line.707"></a>
<FONT color="green">708</FONT>         * sine&lt;/a&gt;<a name="line.708"></a>
<FONT color="green">709</FONT>         * of this complex number.<a name="line.709"></a>
<FONT color="green">710</FONT>         * &lt;p&gt;<a name="line.710"></a>
<FONT color="green">711</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.711"></a>
<FONT color="green">712</FONT>         * &lt;code&gt; sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i&lt;/code&gt;&lt;/pre&gt;<a name="line.712"></a>
<FONT color="green">713</FONT>         * where the (real) functions on the right-hand side are<a name="line.713"></a>
<FONT color="green">714</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.714"></a>
<FONT color="green">715</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.715"></a>
<FONT color="green">716</FONT>         * &lt;p&gt;<a name="line.716"></a>
<FONT color="green">717</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.717"></a>
<FONT color="green">718</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.718"></a>
<FONT color="green">719</FONT>         * &lt;p&gt;<a name="line.719"></a>
<FONT color="green">720</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.720"></a>
<FONT color="green">721</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.721"></a>
<FONT color="green">722</FONT>         * Examples: <a name="line.722"></a>
<FONT color="green">723</FONT>         * &lt;code&gt;<a name="line.723"></a>
<FONT color="green">724</FONT>         * sin(1 &amp;plusmn; INFINITY i) = 1 &amp;plusmn; INFINITY i<a name="line.724"></a>
<FONT color="green">725</FONT>         * sin(&amp;plusmn;INFINITY + i) = NaN + NaN i<a name="line.725"></a>
<FONT color="green">726</FONT>         * sin(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.726"></a>
<FONT color="green">727</FONT>         * <a name="line.727"></a>
<FONT color="green">728</FONT>         * @return the sine of this complex number.<a name="line.728"></a>
<FONT color="green">729</FONT>         * @since 1.2<a name="line.729"></a>
<FONT color="green">730</FONT>         */<a name="line.730"></a>
<FONT color="green">731</FONT>        public Complex sin() {<a name="line.731"></a>
<FONT color="green">732</FONT>            if (isNaN()) {<a name="line.732"></a>
<FONT color="green">733</FONT>                return Complex.NaN;<a name="line.733"></a>
<FONT color="green">734</FONT>            }<a name="line.734"></a>
<FONT color="green">735</FONT>            <a name="line.735"></a>
<FONT color="green">736</FONT>            return createComplex(Math.sin(real) * MathUtils.cosh(imaginary),<a name="line.736"></a>
<FONT color="green">737</FONT>                Math.cos(real) * MathUtils.sinh(imaginary));<a name="line.737"></a>
<FONT color="green">738</FONT>        }<a name="line.738"></a>
<FONT color="green">739</FONT>        <a name="line.739"></a>
<FONT color="green">740</FONT>        /**<a name="line.740"></a>
<FONT color="green">741</FONT>         * Compute the <a name="line.741"></a>
<FONT color="green">742</FONT>         * &lt;a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top"&gt;<a name="line.742"></a>
<FONT color="green">743</FONT>         * hyperbolic sine&lt;/a&gt; of this complex number.<a name="line.743"></a>
<FONT color="green">744</FONT>         * &lt;p&gt;<a name="line.744"></a>
<FONT color="green">745</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.745"></a>
<FONT color="green">746</FONT>         * &lt;code&gt; sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i&lt;/code&gt;&lt;/pre&gt;<a name="line.746"></a>
<FONT color="green">747</FONT>         * where the (real) functions on the right-hand side are<a name="line.747"></a>
<FONT color="green">748</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.748"></a>
<FONT color="green">749</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.749"></a>
<FONT color="green">750</FONT>         * &lt;p&gt;<a name="line.750"></a>
<FONT color="green">751</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.751"></a>
<FONT color="green">752</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.752"></a>
<FONT color="green">753</FONT>         * &lt;p&gt;<a name="line.753"></a>
<FONT color="green">754</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.754"></a>
<FONT color="green">755</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.755"></a>
<FONT color="green">756</FONT>         * Examples: <a name="line.756"></a>
<FONT color="green">757</FONT>         * &lt;code&gt;<a name="line.757"></a>
<FONT color="green">758</FONT>         * sinh(1 &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.758"></a>
<FONT color="green">759</FONT>         * sinh(&amp;plusmn;INFINITY + i) = &amp;plusmn; INFINITY + INFINITY i<a name="line.759"></a>
<FONT color="green">760</FONT>         * sinh(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.760"></a>
<FONT color="green">761</FONT>         * <a name="line.761"></a>
<FONT color="green">762</FONT>         * @return the hyperbolic sine of this complex number<a name="line.762"></a>
<FONT color="green">763</FONT>         * @since 1.2<a name="line.763"></a>
<FONT color="green">764</FONT>         */<a name="line.764"></a>
<FONT color="green">765</FONT>        public Complex sinh() {<a name="line.765"></a>
<FONT color="green">766</FONT>            if (isNaN()) {<a name="line.766"></a>
<FONT color="green">767</FONT>                return Complex.NaN;<a name="line.767"></a>
<FONT color="green">768</FONT>            }<a name="line.768"></a>
<FONT color="green">769</FONT>            <a name="line.769"></a>
<FONT color="green">770</FONT>            return createComplex(MathUtils.sinh(real) * Math.cos(imaginary),<a name="line.770"></a>
<FONT color="green">771</FONT>                MathUtils.cosh(real) * Math.sin(imaginary));<a name="line.771"></a>
<FONT color="green">772</FONT>        }<a name="line.772"></a>
<FONT color="green">773</FONT>        <a name="line.773"></a>
<FONT color="green">774</FONT>        /**<a name="line.774"></a>
<FONT color="green">775</FONT>         * Compute the <a name="line.775"></a>
<FONT color="green">776</FONT>         * &lt;a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"&gt;<a name="line.776"></a>
<FONT color="green">777</FONT>         * square root&lt;/a&gt; of this complex number.<a name="line.777"></a>
<FONT color="green">778</FONT>         * &lt;p&gt;<a name="line.778"></a>
<FONT color="green">779</FONT>         * Implements the following algorithm to compute &lt;code&gt;sqrt(a + bi)&lt;/code&gt;: <a name="line.779"></a>
<FONT color="green">780</FONT>         * &lt;ol&gt;&lt;li&gt;Let &lt;code&gt;t = sqrt((|a| + |a + bi|) / 2)&lt;/code&gt;&lt;/li&gt;<a name="line.780"></a>
<FONT color="green">781</FONT>         * &lt;li&gt;&lt;pre&gt;if &lt;code&gt; a &amp;#8805; 0&lt;/code&gt; return &lt;code&gt;t + (b/2t)i&lt;/code&gt;<a name="line.781"></a>
<FONT color="green">782</FONT>         *  else return &lt;code&gt;|b|/2t + sign(b)t i &lt;/code&gt;&lt;/pre&gt;&lt;/li&gt;<a name="line.782"></a>
<FONT color="green">783</FONT>         * &lt;/ol&gt;<a name="line.783"></a>
<FONT color="green">784</FONT>         * where &lt;ul&gt;<a name="line.784"></a>
<FONT color="green">785</FONT>         * &lt;li&gt;&lt;code&gt;|a| = {@link Math#abs}(a)&lt;/code&gt;&lt;/li&gt;<a name="line.785"></a>
<FONT color="green">786</FONT>         * &lt;li&gt;&lt;code&gt;|a + bi| = {@link Complex#abs}(a + bi) &lt;/code&gt;&lt;/li&gt;<a name="line.786"></a>
<FONT color="green">787</FONT>         * &lt;li&gt;&lt;code&gt;sign(b) =  {@link MathUtils#indicator}(b) &lt;/code&gt;<a name="line.787"></a>
<FONT color="green">788</FONT>         * &lt;/ul&gt;&lt;/p&gt;<a name="line.788"></a>
<FONT color="green">789</FONT>         * &lt;p&gt;<a name="line.789"></a>
<FONT color="green">790</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.790"></a>
<FONT color="green">791</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.791"></a>
<FONT color="green">792</FONT>         * &lt;p&gt;<a name="line.792"></a>
<FONT color="green">793</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.793"></a>
<FONT color="green">794</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.794"></a>
<FONT color="green">795</FONT>         * Examples: <a name="line.795"></a>
<FONT color="green">796</FONT>         * &lt;code&gt;<a name="line.796"></a>
<FONT color="green">797</FONT>         * sqrt(1 &amp;plusmn; INFINITY i) = INFINITY + NaN i<a name="line.797"></a>
<FONT color="green">798</FONT>         * sqrt(INFINITY + i) = INFINITY + 0i<a name="line.798"></a>
<FONT color="green">799</FONT>         * sqrt(-INFINITY + i) = 0 + INFINITY i<a name="line.799"></a>
<FONT color="green">800</FONT>         * sqrt(INFINITY &amp;plusmn; INFINITY i) = INFINITY + NaN i<a name="line.800"></a>
<FONT color="green">801</FONT>         * sqrt(-INFINITY &amp;plusmn; INFINITY i) = NaN &amp;plusmn; INFINITY i<a name="line.801"></a>
<FONT color="green">802</FONT>         * &lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.802"></a>
<FONT color="green">803</FONT>         * <a name="line.803"></a>
<FONT color="green">804</FONT>         * @return the square root of this complex number<a name="line.804"></a>
<FONT color="green">805</FONT>         * @since 1.2<a name="line.805"></a>
<FONT color="green">806</FONT>         */<a name="line.806"></a>
<FONT color="green">807</FONT>        public Complex sqrt() {<a name="line.807"></a>
<FONT color="green">808</FONT>            if (isNaN()) {<a name="line.808"></a>
<FONT color="green">809</FONT>                return Complex.NaN;<a name="line.809"></a>
<FONT color="green">810</FONT>            }<a name="line.810"></a>
<FONT color="green">811</FONT>            <a name="line.811"></a>
<FONT color="green">812</FONT>            if (real == 0.0 &amp;&amp; imaginary == 0.0) {<a name="line.812"></a>
<FONT color="green">813</FONT>                return createComplex(0.0, 0.0);<a name="line.813"></a>
<FONT color="green">814</FONT>            }<a name="line.814"></a>
<FONT color="green">815</FONT>            <a name="line.815"></a>
<FONT color="green">816</FONT>            double t = Math.sqrt((Math.abs(real) + abs()) / 2.0);<a name="line.816"></a>
<FONT color="green">817</FONT>            if (real &gt;= 0.0) {<a name="line.817"></a>
<FONT color="green">818</FONT>                return createComplex(t, imaginary / (2.0 * t));<a name="line.818"></a>
<FONT color="green">819</FONT>            } else {<a name="line.819"></a>
<FONT color="green">820</FONT>                return createComplex(Math.abs(imaginary) / (2.0 * t),<a name="line.820"></a>
<FONT color="green">821</FONT>                    MathUtils.indicator(imaginary) * t);<a name="line.821"></a>
<FONT color="green">822</FONT>            }<a name="line.822"></a>
<FONT color="green">823</FONT>        }<a name="line.823"></a>
<FONT color="green">824</FONT>        <a name="line.824"></a>
<FONT color="green">825</FONT>        /**<a name="line.825"></a>
<FONT color="green">826</FONT>         * Compute the <a name="line.826"></a>
<FONT color="green">827</FONT>         * &lt;a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"&gt;<a name="line.827"></a>
<FONT color="green">828</FONT>         * square root&lt;/a&gt; of 1 - &lt;code&gt;this&lt;/code&gt;&lt;sup&gt;2&lt;/sup&gt; for this complex<a name="line.828"></a>
<FONT color="green">829</FONT>         * number.<a name="line.829"></a>
<FONT color="green">830</FONT>         * &lt;p&gt;<a name="line.830"></a>
<FONT color="green">831</FONT>         * Computes the result directly as <a name="line.831"></a>
<FONT color="green">832</FONT>         * &lt;code&gt;sqrt(Complex.ONE.subtract(z.multiply(z)))&lt;/code&gt;.&lt;/p&gt;<a name="line.832"></a>
<FONT color="green">833</FONT>         * &lt;p&gt;<a name="line.833"></a>
<FONT color="green">834</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.834"></a>
<FONT color="green">835</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.835"></a>
<FONT color="green">836</FONT>         * &lt;p&gt;<a name="line.836"></a>
<FONT color="green">837</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.837"></a>
<FONT color="green">838</FONT>         * infinite or NaN values returned in parts of the result.&lt;/p&gt;<a name="line.838"></a>
<FONT color="green">839</FONT>         * <a name="line.839"></a>
<FONT color="green">840</FONT>         * @return the square root of 1 - &lt;code&gt;this&lt;/code&gt;&lt;sup&gt;2&lt;/sup&gt;<a name="line.840"></a>
<FONT color="green">841</FONT>         * @since 1.2<a name="line.841"></a>
<FONT color="green">842</FONT>         */<a name="line.842"></a>
<FONT color="green">843</FONT>        public Complex sqrt1z() {<a name="line.843"></a>
<FONT color="green">844</FONT>            return createComplex(1.0, 0.0).subtract(this.multiply(this)).sqrt();<a name="line.844"></a>
<FONT color="green">845</FONT>        }<a name="line.845"></a>
<FONT color="green">846</FONT>        <a name="line.846"></a>
<FONT color="green">847</FONT>        /**<a name="line.847"></a>
<FONT color="green">848</FONT>         * Compute the <a name="line.848"></a>
<FONT color="green">849</FONT>         * &lt;a href="http://mathworld.wolfram.com/Tangent.html" TARGET="_top"&gt;<a name="line.849"></a>
<FONT color="green">850</FONT>         * tangent&lt;/a&gt; of this complex number.<a name="line.850"></a>
<FONT color="green">851</FONT>         * &lt;p&gt;<a name="line.851"></a>
<FONT color="green">852</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.852"></a>
<FONT color="green">853</FONT>         * &lt;code&gt;tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i&lt;/code&gt;&lt;/pre&gt;<a name="line.853"></a>
<FONT color="green">854</FONT>         * where the (real) functions on the right-hand side are<a name="line.854"></a>
<FONT color="green">855</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.855"></a>
<FONT color="green">856</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.856"></a>
<FONT color="green">857</FONT>         * &lt;p&gt;<a name="line.857"></a>
<FONT color="green">858</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.858"></a>
<FONT color="green">859</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.859"></a>
<FONT color="green">860</FONT>         * &lt;p&gt;<a name="line.860"></a>
<FONT color="green">861</FONT>         * Infinite (or critical) values in real or imaginary parts of the input may<a name="line.861"></a>
<FONT color="green">862</FONT>         * result in infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.862"></a>
<FONT color="green">863</FONT>         * Examples: <a name="line.863"></a>
<FONT color="green">864</FONT>         * &lt;code&gt;<a name="line.864"></a>
<FONT color="green">865</FONT>         * tan(1 &amp;plusmn; INFINITY i) = 0 + NaN i<a name="line.865"></a>
<FONT color="green">866</FONT>         * tan(&amp;plusmn;INFINITY + i) = NaN + NaN i<a name="line.866"></a>
<FONT color="green">867</FONT>         * tan(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.867"></a>
<FONT color="green">868</FONT>         * tan(&amp;plusmn;&amp;pi;/2 + 0 i) = &amp;plusmn;INFINITY + NaN i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.868"></a>
<FONT color="green">869</FONT>         * <a name="line.869"></a>
<FONT color="green">870</FONT>         * @return the tangent of this complex number<a name="line.870"></a>
<FONT color="green">871</FONT>         * @since 1.2<a name="line.871"></a>
<FONT color="green">872</FONT>         */<a name="line.872"></a>
<FONT color="green">873</FONT>        public Complex tan() {<a name="line.873"></a>
<FONT color="green">874</FONT>            if (isNaN()) {<a name="line.874"></a>
<FONT color="green">875</FONT>                return Complex.NaN;<a name="line.875"></a>
<FONT color="green">876</FONT>            }<a name="line.876"></a>
<FONT color="green">877</FONT>            <a name="line.877"></a>
<FONT color="green">878</FONT>            double real2 = 2.0 * real;<a name="line.878"></a>
<FONT color="green">879</FONT>            double imaginary2 = 2.0 * imaginary;<a name="line.879"></a>
<FONT color="green">880</FONT>            double d = Math.cos(real2) + MathUtils.cosh(imaginary2);<a name="line.880"></a>
<FONT color="green">881</FONT>            <a name="line.881"></a>
<FONT color="green">882</FONT>            return createComplex(Math.sin(real2) / d, MathUtils.sinh(imaginary2) / d);<a name="line.882"></a>
<FONT color="green">883</FONT>        }<a name="line.883"></a>
<FONT color="green">884</FONT>        <a name="line.884"></a>
<FONT color="green">885</FONT>        /**<a name="line.885"></a>
<FONT color="green">886</FONT>         * Compute the<a name="line.886"></a>
<FONT color="green">887</FONT>         * &lt;a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top"&gt;<a name="line.887"></a>
<FONT color="green">888</FONT>         * hyperbolic tangent&lt;/a&gt; of this complex number.<a name="line.888"></a>
<FONT color="green">889</FONT>         * &lt;p&gt;<a name="line.889"></a>
<FONT color="green">890</FONT>         * Implements the formula: &lt;pre&gt;<a name="line.890"></a>
<FONT color="green">891</FONT>         * &lt;code&gt;tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i&lt;/code&gt;&lt;/pre&gt;<a name="line.891"></a>
<FONT color="green">892</FONT>         * where the (real) functions on the right-hand side are<a name="line.892"></a>
<FONT color="green">893</FONT>         * {@link java.lang.Math#sin}, {@link java.lang.Math#cos}, <a name="line.893"></a>
<FONT color="green">894</FONT>         * {@link MathUtils#cosh} and {@link MathUtils#sinh}.&lt;/p&gt;<a name="line.894"></a>
<FONT color="green">895</FONT>         * &lt;p&gt;<a name="line.895"></a>
<FONT color="green">896</FONT>         * Returns {@link Complex#NaN} if either real or imaginary part of the <a name="line.896"></a>
<FONT color="green">897</FONT>         * input argument is &lt;code&gt;NaN&lt;/code&gt;.&lt;/p&gt;<a name="line.897"></a>
<FONT color="green">898</FONT>         * &lt;p&gt;<a name="line.898"></a>
<FONT color="green">899</FONT>         * Infinite values in real or imaginary parts of the input may result in<a name="line.899"></a>
<FONT color="green">900</FONT>         * infinite or NaN values returned in parts of the result.&lt;pre&gt;<a name="line.900"></a>
<FONT color="green">901</FONT>         * Examples: <a name="line.901"></a>
<FONT color="green">902</FONT>         * &lt;code&gt;<a name="line.902"></a>
<FONT color="green">903</FONT>         * tanh(1 &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.903"></a>
<FONT color="green">904</FONT>         * tanh(&amp;plusmn;INFINITY + i) = NaN + 0 i<a name="line.904"></a>
<FONT color="green">905</FONT>         * tanh(&amp;plusmn;INFINITY &amp;plusmn; INFINITY i) = NaN + NaN i<a name="line.905"></a>
<FONT color="green">906</FONT>         * tanh(0 + (&amp;pi;/2)i) = NaN + INFINITY i&lt;/code&gt;&lt;/pre&gt;&lt;/p&gt;<a name="line.906"></a>
<FONT color="green">907</FONT>         *<a name="line.907"></a>
<FONT color="green">908</FONT>         * @return the hyperbolic tangent of this complex number<a name="line.908"></a>
<FONT color="green">909</FONT>         * @since 1.2<a name="line.909"></a>
<FONT color="green">910</FONT>         */<a name="line.910"></a>
<FONT color="green">911</FONT>        public Complex tanh() {<a name="line.911"></a>
<FONT color="green">912</FONT>            if (isNaN()) {<a name="line.912"></a>
<FONT color="green">913</FONT>                return Complex.NaN;<a name="line.913"></a>
<FONT color="green">914</FONT>            }<a name="line.914"></a>
<FONT color="green">915</FONT>            <a name="line.915"></a>
<FONT color="green">916</FONT>            double real2 = 2.0 * real;<a name="line.916"></a>
<FONT color="green">917</FONT>            double imaginary2 = 2.0 * imaginary;<a name="line.917"></a>
<FONT color="green">918</FONT>            double d = MathUtils.cosh(real2) + Math.cos(imaginary2);<a name="line.918"></a>
<FONT color="green">919</FONT>            <a name="line.919"></a>
<FONT color="green">920</FONT>            return createComplex(MathUtils.sinh(real2) / d, Math.sin(imaginary2) / d);<a name="line.920"></a>
<FONT color="green">921</FONT>        }<a name="line.921"></a>
<FONT color="green">922</FONT>        <a name="line.922"></a>
<FONT color="green">923</FONT>        <a name="line.923"></a>
<FONT color="green">924</FONT>        <a name="line.924"></a>
<FONT color="green">925</FONT>        /**<a name="line.925"></a>
<FONT color="green">926</FONT>         * &lt;p&gt;Compute the argument of this complex number.<a name="line.926"></a>
<FONT color="green">927</FONT>         * &lt;/p&gt;<a name="line.927"></a>
<FONT color="green">928</FONT>         * &lt;p&gt;The argument is the angle phi between the positive real axis and the point<a name="line.928"></a>
<FONT color="green">929</FONT>         * representing this number in the complex plane. The value returned is between -PI (not inclusive) <a name="line.929"></a>
<FONT color="green">930</FONT>         * and PI (inclusive), with negative values returned for numbers with negative imaginary parts.<a name="line.930"></a>
<FONT color="green">931</FONT>         * &lt;/p&gt;<a name="line.931"></a>
<FONT color="green">932</FONT>         * &lt;p&gt;If either real or imaginary part (or both) is NaN, NaN is returned.  Infinite parts are handled<a name="line.932"></a>
<FONT color="green">933</FONT>         * as java.Math.atan2 handles them, essentially treating finite parts as zero in the presence of<a name="line.933"></a>
<FONT color="green">934</FONT>         * an infinite coordinate and returning a multiple of pi/4 depending on the signs of the infinite<a name="line.934"></a>
<FONT color="green">935</FONT>         * parts.  See the javadoc for java.Math.atan2 for full details.&lt;/p&gt;<a name="line.935"></a>
<FONT color="green">936</FONT>         * <a name="line.936"></a>
<FONT color="green">937</FONT>         * @return the argument of this complex number<a name="line.937"></a>
<FONT color="green">938</FONT>         */<a name="line.938"></a>
<FONT color="green">939</FONT>        public double getArgument() {<a name="line.939"></a>
<FONT color="green">940</FONT>            return Math.atan2(getImaginary(), getReal());<a name="line.940"></a>
<FONT color="green">941</FONT>        }<a name="line.941"></a>
<FONT color="green">942</FONT>        <a name="line.942"></a>
<FONT color="green">943</FONT>        /**<a name="line.943"></a>
<FONT color="green">944</FONT>         * &lt;p&gt;Computes the n-th roots of this complex number.<a name="line.944"></a>
<FONT color="green">945</FONT>         * &lt;/p&gt;<a name="line.945"></a>
<FONT color="green">946</FONT>         * &lt;p&gt;The nth roots are defined by the formula: &lt;pre&gt;<a name="line.946"></a>
<FONT color="green">947</FONT>         * &lt;code&gt; z&lt;sub&gt;k&lt;/sub&gt; = abs&lt;sup&gt; 1/n&lt;/sup&gt; (cos(phi + 2&amp;pi;k/n) + i (sin(phi + 2&amp;pi;k/n))&lt;/code&gt;&lt;/pre&gt;<a name="line.947"></a>
<FONT color="green">948</FONT>         * for &lt;i&gt;&lt;code&gt;k=0, 1, ..., n-1&lt;/code&gt;&lt;/i&gt;, where &lt;code&gt;abs&lt;/code&gt; and &lt;code&gt;phi&lt;/code&gt; are<a name="line.948"></a>
<FONT color="green">949</FONT>         * respectively the {@link #abs() modulus} and {@link #getArgument() argument} of this complex number.<a name="line.949"></a>
<FONT color="green">950</FONT>         * &lt;/p&gt;<a name="line.950"></a>
<FONT color="green">951</FONT>         * &lt;p&gt;If one or both parts of this complex number is NaN, a list with just one element,<a name="line.951"></a>
<FONT color="green">952</FONT>         *  {@link #NaN} is returned.&lt;/p&gt;<a name="line.952"></a>
<FONT color="green">953</FONT>         * &lt;p&gt;if neither part is NaN, but at least one part is infinite, the result is a one-element<a name="line.953"></a>
<FONT color="green">954</FONT>         * list containing {@link #INF}.&lt;/p&gt;<a name="line.954"></a>
<FONT color="green">955</FONT>         * <a name="line.955"></a>
<FONT color="green">956</FONT>         * @param n degree of root<a name="line.956"></a>
<FONT color="green">957</FONT>         * @return List&lt;Complex&gt; all nth roots of this complex number<a name="line.957"></a>
<FONT color="green">958</FONT>         * @throws IllegalArgumentException if parameter n is less than or equal to 0<a name="line.958"></a>
<FONT color="green">959</FONT>         * @since 2.0<a name="line.959"></a>
<FONT color="green">960</FONT>         */<a name="line.960"></a>
<FONT color="green">961</FONT>        public List&lt;Complex&gt; nthRoot(int n) throws IllegalArgumentException {<a name="line.961"></a>
<FONT color="green">962</FONT>    <a name="line.962"></a>
<FONT color="green">963</FONT>            if (n &lt;= 0) {<a name="line.963"></a>
<FONT color="green">964</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.964"></a>
<FONT color="green">965</FONT>                        "cannot compute nth root for null or negative n: {0}",<a name="line.965"></a>
<FONT color="green">966</FONT>                        n);<a name="line.966"></a>
<FONT color="green">967</FONT>            }<a name="line.967"></a>
<FONT color="green">968</FONT>            <a name="line.968"></a>
<FONT color="green">969</FONT>            List&lt;Complex&gt; result = new ArrayList&lt;Complex&gt;();<a name="line.969"></a>
<FONT color="green">970</FONT>            <a name="line.970"></a>
<FONT color="green">971</FONT>            if (isNaN()) {<a name="line.971"></a>
<FONT color="green">972</FONT>                result.add(Complex.NaN);<a name="line.972"></a>
<FONT color="green">973</FONT>                return result;<a name="line.973"></a>
<FONT color="green">974</FONT>            }<a name="line.974"></a>
<FONT color="green">975</FONT>            <a name="line.975"></a>
<FONT color="green">976</FONT>            if (isInfinite()) {<a name="line.976"></a>
<FONT color="green">977</FONT>                result.add(Complex.INF);<a name="line.977"></a>
<FONT color="green">978</FONT>                return result;<a name="line.978"></a>
<FONT color="green">979</FONT>            }<a name="line.979"></a>
<FONT color="green">980</FONT>    <a name="line.980"></a>
<FONT color="green">981</FONT>            // nth root of abs -- faster / more accurate to use a solver here?<a name="line.981"></a>
<FONT color="green">982</FONT>            final double nthRootOfAbs = Math.pow(abs(), 1.0 / n);<a name="line.982"></a>
<FONT color="green">983</FONT>    <a name="line.983"></a>
<FONT color="green">984</FONT>            // Compute nth roots of complex number with k = 0, 1, ... n-1<a name="line.984"></a>
<FONT color="green">985</FONT>            final double nthPhi = getArgument()/n;<a name="line.985"></a>
<FONT color="green">986</FONT>            final double slice = 2 * Math.PI / n;<a name="line.986"></a>
<FONT color="green">987</FONT>            double innerPart = nthPhi;<a name="line.987"></a>
<FONT color="green">988</FONT>            for (int k = 0; k &lt; n ; k++) {<a name="line.988"></a>
<FONT color="green">989</FONT>                // inner part<a name="line.989"></a>
<FONT color="green">990</FONT>                final double realPart      = nthRootOfAbs *  Math.cos(innerPart);<a name="line.990"></a>
<FONT color="green">991</FONT>                final double imaginaryPart = nthRootOfAbs *  Math.sin(innerPart);<a name="line.991"></a>
<FONT color="green">992</FONT>                result.add(createComplex(realPart, imaginaryPart));<a name="line.992"></a>
<FONT color="green">993</FONT>                innerPart += slice;<a name="line.993"></a>
<FONT color="green">994</FONT>            }<a name="line.994"></a>
<FONT color="green">995</FONT>    <a name="line.995"></a>
<FONT color="green">996</FONT>            return result;<a name="line.996"></a>
<FONT color="green">997</FONT>        }<a name="line.997"></a>
<FONT color="green">998</FONT>    <a name="line.998"></a>
<FONT color="green">999</FONT>        /**<a name="line.999"></a>
<FONT color="green">1000</FONT>         * Create a complex number given the real and imaginary parts.<a name="line.1000"></a>
<FONT color="green">1001</FONT>         *<a name="line.1001"></a>
<FONT color="green">1002</FONT>         * @param real the real part<a name="line.1002"></a>
<FONT color="green">1003</FONT>         * @param imaginary the imaginary part<a name="line.1003"></a>
<FONT color="green">1004</FONT>         * @return a new complex number instance<a name="line.1004"></a>
<FONT color="green">1005</FONT>         * @since 1.2<a name="line.1005"></a>
<FONT color="green">1006</FONT>         */<a name="line.1006"></a>
<FONT color="green">1007</FONT>        protected Complex createComplex(double real, double imaginary) {<a name="line.1007"></a>
<FONT color="green">1008</FONT>            return new Complex(real, imaginary);<a name="line.1008"></a>
<FONT color="green">1009</FONT>        }<a name="line.1009"></a>
<FONT color="green">1010</FONT>    <a name="line.1010"></a>
<FONT color="green">1011</FONT>        /**<a name="line.1011"></a>
<FONT color="green">1012</FONT>         * &lt;p&gt;Resolve the transient fields in a deserialized Complex Object.&lt;/p&gt;<a name="line.1012"></a>
<FONT color="green">1013</FONT>         * &lt;p&gt;Subclasses will need to override {@link #createComplex} to deserialize properly&lt;/p&gt; <a name="line.1013"></a>
<FONT color="green">1014</FONT>         * @return A Complex instance with all fields resolved.<a name="line.1014"></a>
<FONT color="green">1015</FONT>         * @since 2.0<a name="line.1015"></a>
<FONT color="green">1016</FONT>         */<a name="line.1016"></a>
<FONT color="green">1017</FONT>        protected final Object readResolve() {<a name="line.1017"></a>
<FONT color="green">1018</FONT>            return createComplex(real, imaginary);<a name="line.1018"></a>
<FONT color="green">1019</FONT>        }<a name="line.1019"></a>
<FONT color="green">1020</FONT>        <a name="line.1020"></a>
<FONT color="green">1021</FONT>        /** {@inheritDoc} */<a name="line.1021"></a>
<FONT color="green">1022</FONT>        public ComplexField getField() {<a name="line.1022"></a>
<FONT color="green">1023</FONT>            return ComplexField.getInstance();<a name="line.1023"></a>
<FONT color="green">1024</FONT>        }<a name="line.1024"></a>
<FONT color="green">1025</FONT>    <a name="line.1025"></a>
<FONT color="green">1026</FONT>    }<a name="line.1026"></a>




























































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